1 /*
2 * Copyright 2017-2023 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright 2015-2016 Cryptography Research, Inc.
4 *
5 * Licensed under the Apache License 2.0 (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 *
10 * Originally written by Mike Hamburg
11 */
12
13 #ifndef OSSL_CRYPTO_EC_CURVE448_POINT_448_H
14 #define OSSL_CRYPTO_EC_CURVE448_POINT_448_H
15
16 #include "curve448utils.h"
17 #include "field.h"
18
19 /* Comb config: number of combs, n, t, s. */
20 #define COMBS_N 5
21 #define COMBS_T 5
22 #define COMBS_S 18
23
24 /* Projective Niels coordinates */
25 typedef struct {
26 gf a, b, c;
27 } niels_s, niels_t[1];
28 typedef struct {
29 niels_t n;
30 gf z;
31 } pniels_t[1];
32
33 /* Precomputed base */
34 struct curve448_precomputed_s {
35 niels_t table[COMBS_N << (COMBS_T - 1)];
36 };
37
38 #define C448_SCALAR_LIMBS ((446 - 1) / C448_WORD_BITS + 1)
39
40 /* The number of bits in a scalar */
41 #define C448_SCALAR_BITS 446
42
43 /* Number of bytes in a serialized scalar. */
44 #define C448_SCALAR_BYTES 56
45
46 /* X448 encoding ratio. */
47 #define X448_ENCODE_RATIO 2
48
49 /* Number of bytes in an x448 public key */
50 #define X448_PUBLIC_BYTES 56
51
52 /* Number of bytes in an x448 private key */
53 #define X448_PRIVATE_BYTES 56
54
55 /* Twisted Edwards extended homogeneous coordinates */
56 typedef struct curve448_point_s {
57 gf x, y, z, t;
58 } curve448_point_t[1];
59
60 /* Precomputed table based on a point. Can be trivial implementation. */
61 struct curve448_precomputed_s;
62
63 /* Precomputed table based on a point. Can be trivial implementation. */
64 typedef struct curve448_precomputed_s curve448_precomputed_s;
65
66 /* Scalar is stored packed, because we don't need the speed. */
67 typedef struct curve448_scalar_s {
68 c448_word_t limb[C448_SCALAR_LIMBS];
69 } curve448_scalar_t[1];
70
71 /* A scalar equal to 1. */
72 extern const curve448_scalar_t ossl_curve448_scalar_one;
73
74 /* A scalar equal to 0. */
75 extern const curve448_scalar_t ossl_curve448_scalar_zero;
76
77 /* The identity point on the curve. */
78 extern const curve448_point_t ossl_curve448_point_identity;
79
80 /* Precomputed table for the base point on the curve. */
81 extern const struct curve448_precomputed_s *ossl_curve448_precomputed_base;
82 extern const niels_t *ossl_curve448_wnaf_base;
83
84 /*
85 * Read a scalar from wire format or from bytes.
86 *
87 * ser (in): Serialized form of a scalar.
88 * out (out): Deserialized form.
89 *
90 * Returns:
91 * C448_SUCCESS: The scalar was correctly encoded.
92 * C448_FAILURE: The scalar was greater than the modulus, and has been reduced
93 * modulo that modulus.
94 */
95 c448_error_t
96 ossl_curve448_scalar_decode(curve448_scalar_t out,
97 const unsigned char ser[C448_SCALAR_BYTES]);
98
99 /*
100 * Read a scalar from wire format or from bytes. Reduces mod scalar prime.
101 *
102 * ser (in): Serialized form of a scalar.
103 * ser_len (in): Length of serialized form.
104 * out (out): Deserialized form.
105 */
106 void ossl_curve448_scalar_decode_long(curve448_scalar_t out,
107 const unsigned char *ser, size_t ser_len);
108
109 /*
110 * Serialize a scalar to wire format.
111 *
112 * ser (out): Serialized form of a scalar.
113 * s (in): Deserialized scalar.
114 */
115 void ossl_curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
116 const curve448_scalar_t s);
117
118 /*
119 * Add two scalars. |a|, |b| and |out| may alias each other.
120 *
121 * a (in): One scalar.
122 * b (in): Another scalar.
123 * out (out): a+b.
124 */
125 void ossl_curve448_scalar_add(curve448_scalar_t out,
126 const curve448_scalar_t a, const curve448_scalar_t b);
127
128 /*
129 * Subtract two scalars. |a|, |b| and |out| may alias each other.
130 * a (in): One scalar.
131 * b (in): Another scalar.
132 * out (out): a-b.
133 */
134 void ossl_curve448_scalar_sub(curve448_scalar_t out,
135 const curve448_scalar_t a, const curve448_scalar_t b);
136
137 /*
138 * Multiply two scalars. |a|, |b| and |out| may alias each other.
139 *
140 * a (in): One scalar.
141 * b (in): Another scalar.
142 * out (out): a*b.
143 */
144 void ossl_curve448_scalar_mul(curve448_scalar_t out,
145 const curve448_scalar_t a, const curve448_scalar_t b);
146
147 /*
148 * Halve a scalar. |a| and |out| may alias each other.
149 *
150 * a (in): A scalar.
151 * out (out): a/2.
152 */
153 void ossl_curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a);
154
155 /*
156 * Copy a scalar. The scalars may alias each other, in which case this
157 * function does nothing.
158 *
159 * a (in): A scalar.
160 * out (out): Will become a copy of a.
161 */
curve448_scalar_copy(curve448_scalar_t out,const curve448_scalar_t a)162 static ossl_inline void curve448_scalar_copy(curve448_scalar_t out,
163 const curve448_scalar_t a)
164 {
165 *out = *a;
166 }
167
168 /*
169 * Copy a point. The input and output may alias, in which case this function
170 * does nothing.
171 *
172 * a (out): A copy of the point.
173 * b (in): Any point.
174 */
curve448_point_copy(curve448_point_t a,const curve448_point_t b)175 static ossl_inline void curve448_point_copy(curve448_point_t a,
176 const curve448_point_t b)
177 {
178 *a = *b;
179 }
180
181 /*
182 * Test whether two points are equal. If yes, return C448_TRUE, else return
183 * C448_FALSE.
184 *
185 * a (in): A point.
186 * b (in): Another point.
187 *
188 * Returns:
189 * C448_TRUE: The points are equal.
190 * C448_FALSE: The points are not equal.
191 */
192 __owur c448_bool_t
193 ossl_curve448_point_eq(const curve448_point_t a,
194 const curve448_point_t b);
195
196 /*
197 * Double a point. Equivalent to curve448_point_add(two_a,a,a), but potentially
198 * faster.
199 *
200 * two_a (out): The sum a+a.
201 * a (in): A point.
202 */
203 void ossl_curve448_point_double(curve448_point_t two_a, const curve448_point_t a);
204
205 /*
206 * RFC 7748 Diffie-Hellman scalarmul. This function uses a different
207 * (non-Decaf) encoding.
208 *
209 * out (out): The scaled point base*scalar
210 * base (in): The point to be scaled.
211 * scalar (in): The scalar to multiply by.
212 *
213 * Returns:
214 * C448_SUCCESS: The scalarmul succeeded.
215 * C448_FAILURE: The scalarmul didn't succeed, because the base point is in a
216 * small subgroup.
217 */
218 __owur c448_error_t
219 ossl_x448_int(uint8_t out[X448_PUBLIC_BYTES],
220 const uint8_t base[X448_PUBLIC_BYTES],
221 const uint8_t scalar[X448_PRIVATE_BYTES]);
222
223 /*
224 * Multiply a point by X448_ENCODE_RATIO, then encode it like RFC 7748.
225 *
226 * This function is mainly used internally, but is exported in case
227 * it will be useful.
228 *
229 * The ratio is necessary because the internal representation doesn't
230 * track the cofactor information, so on output we must clear the cofactor.
231 * This would multiply by the cofactor, but in fact internally points are always
232 * even, so it multiplies by half the cofactor instead.
233 *
234 * As it happens, this aligns with the base point definitions; that is,
235 * if you pass the Decaf/Ristretto base point to this function, the result
236 * will be X448_ENCODE_RATIO times the X448
237 * base point.
238 *
239 * out (out): The scaled and encoded point.
240 * p (in): The point to be scaled and encoded.
241 */
242 void ossl_curve448_point_mul_by_ratio_and_encode_like_x448(
243 uint8_t out[X448_PUBLIC_BYTES],
244 const curve448_point_t p);
245
246 /*
247 * RFC 7748 Diffie-Hellman base point scalarmul. This function uses a different
248 * (non-Decaf) encoding.
249 *
250 * out (out): The scaled point base*scalar
251 * scalar (in): The scalar to multiply by.
252 */
253 void ossl_x448_derive_public_key(uint8_t out[X448_PUBLIC_BYTES],
254 const uint8_t scalar[X448_PRIVATE_BYTES]);
255
256 /*
257 * Multiply a precomputed base point by a scalar: out = scalar*base.
258 *
259 * scaled (out): The scaled point base*scalar
260 * base (in): The point to be scaled.
261 * scalar (in): The scalar to multiply by.
262 */
263 void ossl_curve448_precomputed_scalarmul(curve448_point_t scaled,
264 const curve448_precomputed_s *base,
265 const curve448_scalar_t scalar);
266
267 /*
268 * Multiply two base points by two scalars:
269 * combo = scalar1*curve448_point_base + scalar2*base2.
270 *
271 * Otherwise equivalent to curve448_point_double_scalarmul, but may be
272 * faster at the expense of being variable time.
273 *
274 * combo (out): The linear combination scalar1*base + scalar2*base2.
275 * scalar1 (in): A first scalar to multiply by.
276 * base2 (in): A second point to be scaled.
277 * scalar2 (in) A second scalar to multiply by.
278 *
279 * Warning: This function takes variable time, and may leak the scalars used.
280 * It is designed for signature verification.
281 */
282 void ossl_curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
283 const curve448_scalar_t scalar1,
284 const curve448_point_t base2,
285 const curve448_scalar_t scalar2);
286
287 /*
288 * Test that a point is valid, for debugging purposes.
289 *
290 * to_test (in): The point to test.
291 *
292 * Returns:
293 * C448_TRUE The point is valid.
294 * C448_FALSE The point is invalid.
295 */
296 __owur c448_bool_t
297 ossl_curve448_point_valid(const curve448_point_t to_test);
298
299 /* Overwrite scalar with zeros. */
300 void ossl_curve448_scalar_destroy(curve448_scalar_t scalar);
301
302 /* Overwrite point with zeros. */
303 void ossl_curve448_point_destroy(curve448_point_t point);
304
305 #endif /* OSSL_CRYPTO_EC_CURVE448_POINT_448_H */
306